Nope, can't say that I have ever seen or learnt anything in real life where improvement includes allowing you to do as poorly as the worst novice (or even one of their worse, rather than average, attempts) in conditions no different from normal.
It would be like my beating an Olympic sprinter in a sprint. That just won't happen, the floor has gone up at some point.
I liked Flickerdart's thing. DC is sort of analogous to AC, with some other thing representing the number of points in excess of that DC you need to accumulate to finish it. Or something like that.It therefore follows that skills in D&D should use a different mechanic so that we can model skills on a continuum of success and failure and skill checks are less "did you succeed" and more "how much (or little) did you accomplish".